Gauss–Newton algorithm
The Gauss–Newton algorithm is used to solve non-linear least squares problems, which is equivalent to minimizing a sum of squared function values. It is an extension of Newton's method for finding a minimum of a non-linear function. Since a sum of squares must be nonnegative, the algorithm can be viewed as using Newton's method to iteratively approximate zeroes of the sum, and thus minimizing the sum. It has the advantage that second derivatives, which can be challenging to compute, are not required.
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- enThe Gauss–Newton algorithm is used to solve non-linear least squares problems, which is equivalent to minimizing a sum of squared function values. It is an extension of Newton's method for finding a minimum of a non-linear function. Since a sum of squares must be nonnegative, the algorithm can be viewed as using Newton's method to iteratively approximate zeroes of the sum, and thus minimizing the sum. It has the advantage that second derivatives, which can be challenging to compute, are not required.
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- enThe Gauss–Newton algorithm is used to solve non-linear least squares problems, which is equivalent to minimizing a sum of squared function values. It is an extension of Newton's method for finding a minimum of a non-linear function. Since a sum of squares must be nonnegative, the algorithm can be viewed as using Newton's method to iteratively approximate zeroes of the sum, and thus minimizing the sum. It has the advantage that second derivatives, which can be challenging to compute, are not required. Non-linear least squares problems arise, for instance, in non-linear regression, where parameters in a model are sought such that the model is in good agreement with available observations. The method is named after the mathematicians Carl Friedrich Gauss and Isaac Newton, and first appeared in Gauss' 1809 work Theoria motus corporum coelestium in sectionibus conicis solem ambientum.
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- enGauss–Newton algorithm
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- Backtracking line search
- BFGS method
- Carl Friedrich Gauss
- Category:Least squares
- Category:Optimization algorithms and methods
- Category:Statistical algorithms
- Cholesky decomposition
- Column vectors
- Conjugate gradient
- Conjugate gradient method
- Davidon–Fletcher–Powell formula
- Descent direction
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- Function (mathematics)
- Gauss–Newton algorithm
- Goldstein conditions
- Gradient
- Gradient descent
- Hessian matrix
- Ill-conditioned
- Isaac Newton
- Iterative method
- Jacobian matrix
- John Wiley & Sons
- Levenberg–Marquardt algorithm
- Linear approximation
- Linear least squares (mathematics)
- Line search
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- Matrix transpose
- Maxima and minima
- Moore–Penrose pseudoinverse
- Newton's method
- Newton's method in optimization
- Non-linear least squares
- Non-linear regression
- Parallel computing
- QR factorization
- Quasi-Newton method
- Rate of convergence
- Residual (statistics)
- Sparse matrix
- Stationary point
- Steepest descent
- Taylor's theorem
- Trust region
- Wolfe conditions
- Zero of a function
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- Algorisme de Gauss-Newton
- Algorithme de Gauss-Newton
- Algoritma Gauss-Newton
- Algoritmo de Gauss-Newton
- Algoritmo de Gauss-Newton
- Algoritmo di Gauss-Newton
- Gauss–Newton algoritmen
- Gauß-Newton-Verfahren
- m.04cqdk
- Q1496373
- VfT6
- Алгоритм Гаусса — Ньютона
- Алгоритъм на Гаус-Нютон
- אלגוריתם גאוס-ניוטון
- خوارزمية جاوس ونيوتن
- ガウス・ニュートン法
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- Category:Least squares
- Category:Optimization algorithms and methods
- Category:Statistical algorithms
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